Question

Anna walked from home to school at the speed of 3km/hour. Later that day, she ran home at a speed of 6km/hour. Anna's sister Olga walked to school and back at the same constant speed, and she spent as much time on the road as Anna. What was Olga's speed?

Answer 1

Olga's speed was 6 km/hour.

Step-by-step explanation:

To find Olga's speed, we need to determine the total distance Anna walked to school and back. Since she walked at a speed of 3 km/hour, and the time spent walking is the same as the time Anna spent walking to school and back, we can use the formula:

Total Distance = Speed * Time

Let's denote Olga's speed as 'x' km/hour.

For Anna's trip to school, she walked a distance of 3 km at a speed of 3 km/hour. So, her time is:

Time = Distance / Speed = 3 km / 3 km/hour = 1 hour

For Anna's trip back home, she ran at a speed of 6 km/hour. So, her time is:

Time = Distance / Speed = Distance / 6 km/hour = 1 hour

Since Olga spent the same amount of time on the road as Anna, her total distance is 3 km (one way) + 3 km (for the return) = 6 km.

Using the formula for total distance:

Total Distance = Speed * Time

6 km = x km/hour * 1 hour

Therefore, Olga's speed is 6 km/hour.

Answer 2

Olga's constant speed is 4 km/h. This is calculated by taking the total distance she would travel to school and back, which is the same as Anna, and dividing it by the total time Anna spent on her round trip, assuming the distance between home and school is the same for both of them.

Step-by-step explanation:

To find out Olga's speed, we need to calculate the time Anna took for her trips and then determine how far Olga would have walked in the same amount of time at a constant speed. We know Anna walked to school at 3 km/h and ran back home at 6 km/h.

Let's denote the distance between home and school as d km. The time Anna took to walk to school is t1 = d / 3 hours, and the time to run back is t2 = d / 6 hours. The total time Anna spent is ttotal = t1 + t2 = d / 3 + d / 6 = d / 2 hours, as 1/3 + 1/6 simplifies to 1/2.

Olga spends the same total time ttotal = d / 2 hours on the road. To find her speed v, we know she travels the same distance d to school and d back home, so the total distance is 2d. Using the formula for speed (v = total distance / total time), Olga's speed is v = 2d / (d/2) = 4 km/h.